Creating trails using Animation Nodes by delaying the frame of the following polygons
You can use F-Curves. F-Curves are functions that describe the value of attributes in Blender. So by evaluating the F-Curves of transformation channels at a certain frame, we can get the transformation of the object at that frame.

First, we create a group that computes the transformation of an object as a matrix and returns it. We will assume that only transformation channels are animated and that they are in order for simplicity.



We then create a loop that iterates over a float list that represents the frames we want to evaluate at.



Then we will replicate a line of matrices based on the output matrices of the loop, where the input frames are arithmetic sequence starting from the current frame. We use the indices data from a Grid Mesh to create the polygons between the replicated matrices.



In this node tree, the step size of the sequence controls the length and direction of the trail:



Blend file for AN 2.1: